Given $ m \angle AOB = 7x + 107$, and $ m \angle BOC = 6x + 47$, find $m\angle BOC$. $O$ $A$ $C$ $B$
Answer: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {7x + 107} + {6x + 47} = {180}$ Combine like terms: $ 13x + 154 = 180$ Subtract $154$ from both sides: $ 13x = 26$ Divide both sides by $13$ to find $x$ $ x = 2$ Substitute $2$ for $x$ in the expression that was given for $m\angle BOC$ $ m\angle BOC = 6({2}) + 47$ Simplify: $ {m\angle BOC = 12 + 47}$ So ${m\angle BOC = 59}$.